The quantum Hall effect in graphene samples and the relativistic Dirac effective action

TL;DR

This paper investigates the quantum Hall effect in graphene by analyzing the Dirac effective action under magnetic fields, finite temperature, and density, linking theoretical calculations to experimental Hall conductivity measurements.

Contribution

It introduces a detailed theoretical framework for the Dirac effective action in graphene, connecting quantum field theory with experimental Hall conductivity data.

Findings

Reproduces Hall conductivity in graphene samples at zero temperature.

Shows dependence of Hall conductivity on phase choice in fermionic determinant.

Provides a Lorentz-boosted interpretation of the effective action.

Abstract

We study the Euclidean effective action per unit area and the charge density for a Dirac field in a two--dimensional spatial region, in the presence of a uniform magnetic field perpendicular to the 2D--plane, at finite temperature and density. In the limit of zero temperature we reproduce, after performing an adequate Lorentz boost, the Hall conductivity measured for different kinds of graphene samples, depending upon the phase choice in the fermionic determinant.